When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection

• URL: http://arxiv.org/abs/2507.09716v1
• Date: Sun, 13 Jul 2025 17:25:45 GMT
• Title: When the Weak Becomes Strong: Effective Observables via Time-Symmetric Quantum Selection
• Authors: Mirco A. Mannucci,
• Abstract summary: We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics.<n>We show that the product of these two weak values corresponds to the normalized expectation value of a strong, state-conditioned observable.<n>We illustrate practical applications in quantum information, including state-specific error witnessing in quantum computing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state $\ket{\psi}$ to a post-selected state $\ket{\phi}$, followed by a reverse'' weak measurement. We show that the product of these two weak values corresponds to the normalized expectation value of a strong, state-conditioned observable $B = A P_\psi A$, where $P_\psi = \ket{\psi}\bra{\psi}$ is the projector onto the preselected state. Analyzing the structure of $B$, we demonstrate how it encodes interference information, particularly when $\ket{\psi}$ is a superposition rather than an eigenstate of $A$. This formulation extends naturally to mixed states by replacing $P_\psi$ with a generic density matrix $\rho$, linking the construction to the formalism of generalized quantum measurements. We illustrate practical applications in quantum information, including state-specific error witnessing in quantum computing, and show how the phase of a weak value can be inferred via strong measurements in the pure-state case.

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